"It's not only his responsibility now. It's a team responsibility and he needs to feel free to play and try to help the team. It's a big opportunity for him to show his real skill. He needs to enjoy the game," Pochettino told reporters on Friday.
"He has nothing to show - he just needs to play football. Always with a striker, they need to feel confidence and feel the net. It was a good opportunity for him to score his first official goal with us and that is always important."
Kane, who ended last season as the league's top scorer with 25 goals, was carried off with an ankle injury against Sunderland last weekend.
"Kane is out, we need to assess him every day - he's very positive, we need to do another scan and see how long," Pochettino added.
The former Southampton boss was unsure of the fitness of defender Danny Rose and midfielders Mousa Dembele and Eric Dier for the game at the Riverside Stadium.
Rose suffered a hamstring injury on England duty this month while Dembele and Dier left the field early against Sunderland.
"For Danny, Mousa and Eric, we will see (how they are) today (Friday) in the last training session and then we need to take a decision, so we'll see," Pochettino said.
Tottenham, who finished third in the league last season, lie third in the standings with three wins from five games.
(Reporting by Ian Rodricks in Bengaluru, editing by Ed Osmond)
